| Abstract | The moduli space of Higgs bundles was firstly studied by Hitchin in 1987, where he defined the now so called Hitchin system. In the past 30 years, Hitchin system was shown having rich geometry and one of the most important conjecture about Hitchin system is the topological mirror symmetry conjecture(TMSC) between $\SL_n$ and $\PGL_n$ Hitchin systems. It states that these two Hitchin systems are mirror partners and have the same (stringy) Hodge numbers. This conjecture is posted by Hausel and Thaddeus in 2003 and proved by Groechenig, Wyss and Ziegler in 2020. In this talk, I will review some basic facts about TMSC for Hitchin systems, then introduce the parabolic generalization of TMSC and give a proof by generalizing methods of Groechenig, Wyss and Ziegler to parabolic setting. This is a joint work with Xiaoyu Su and Bin Wang. |
